Question

If $AB=12$ cm, $BC=16$ cm and $AB$ is perpendicular to $BC$, then the radius of the circle passing through the points $A$, $B$ and $C$ is:

• A. $6cm$
• B. $8cm$
• C. $10cm$
• D. $12cm$

Answer 1

The correct option is C $10cm$

Given- $A,B$ & $C$ are points such that $AB=12cm$ and $BC=16cm$ and $BC\perp AB$.

To find out- the radius of the circle passing through $A,B$ & $C=?$

Solution- $BC\perp AB$ i.e $\angle ABC={90}^0$ and $\Delta ABC$ is a right one with $AC$ as hypotenuse. $\therefore AC=\sqrt{{AB}^2+{BC}^2}=\sqrt{{12}^2+{16}^2}cm=20cm$. So the circle passing through $A,B$ & $C$ will have its diameter as $AC$.

$\therefore$ Its radius$=\frac{1}{2}\times 20cm=10cm.$

Ans- Option C.